No abstract

No abstract

No abstract

Geoscientists are confronted with the challenge of assessing nonlinear phenomena that result from multiphysics coupling across multiple scales from the quantum level to the scale of the earth and from femtosecond to the 4.5 Ga of history of our planet. We neglect in this review electromagnetic modelling of the processes in the Earth's core, and focus on four types of couplings that underpin fundamental instabilities in the Earth. These are thermal (T), hydraulic (H), mechanical (M) and chemical (C) processes which are driven and controlled by the transfer of heat to the Earth's surface. Instabilities appear as faults, folds, compaction bands, shear/fault zones, plate boundaries and convective patterns. Convective patterns emerge from buoyancy overcoming viscous drag at a critical Rayleigh number. All other processes emerge from non-conservative thermodynamic forces with a critical critical dissipative source term, which can be characterised by the modified Gruntfest number Gr. These dissipative processes reach a quasi-steady state when, at maximum dissipation, THMC diffusion (Fourier, Darcy, Biot, Fick) balance the source term. The emerging steady state dissipative patterns are defined by the respective diffusion length scales. These length scales provide a fundamental thermodynamic yardstick for measuring instabilities in the Earth. The implementation of a fully coupled THMC multiscale theoretical framework into an applied workflow is still in its early stages. This is largely owing to the four fundamentally different lengths of the THMC diffusion yardsticks spanning micro-metre to tens of kilometres compounded by the additional necessity to consider microstructure information in the formulation of enriched continua for THMC feedback simulations (i.e., micro-structure enriched continuum formulation). Another challenge is to consider the important factor time which implies that the geomaterial often is very far away from initial yield and flowing on a time scale that cannot be accessed in the laboratory. This leads to the requirement of adopting a thermodynamic framework in conjunction with flow theories of plasticity. This framework allows, unlike consistency plasticity, the description of both solid mechanical and fluid dynamic instabilities. In the applications we show the similarity of THMC feedback patterns across scales such as brittle and ductile folds and faults.

[1] A new method is introduced for quantifying the scale and the intensity of strain localization from maps of natural shear zones. The method employs autocorrelation functions to determine local areal scales of geometric homogeneity. These homogenization scales are used to calculate scale-dependent localization fractions of deformed rock. The strain localization intensity is quantified from measurements of mean relative to maximum shear strain. This approach is used to analyze shear zones on different scales from an exposure (Cap de Creus, Spain) of the fossil brittle-to-viscous transition (BVT). Changes in the scaling characteristics of shear zones are interpreted to reflect a time sequence of localization during the evolution of the continental BVT. We show that shear zone scaling is related to inherited anisotropies (older schistosity, lithological layering, pegmatite bodies) and to the predominant mode of deformation (brittle, viscous). The length-towidth ratio of shear zones increases with their length up to the meter scale and decreases for larger length scales as they evolve from isolated shear fractures to interconnected mylonitic shear zones. Variations in strain localization intensity calculated along a single shear zone indicate that such shear zones weakened from their brittle tips to their mylonitic centers, thus driving their propagation and growth to larger scales. Our results imply that the BVT evolves by ''network widening,'' a process whereby strain localizes on progressively larger scales until a dense network of weak, mylonitic layers tens to hundreds of meters wide and hundreds to thousands of meters long forms subparallel to the regional shearing plane.Citation: Schrank, C. E., M. R. Handy, and F. Fusseis (2008), Multiscaling of shear zones and the evolution of the brittle-to-viscous transition in continental crust,